Core competencies are bundles of business processes, technologies and intellectual capital - patents and knowledge which enable a business to do certain things well. Authors Gary Hamel and CK Prahalad (Competing for the Future) talk about 3M as an example. They compete on core competencies relating to knowledge about different types of glue. You'll never see a 3M product development person walking around WH Smiths looking at the different types of glues their competitors make (competitive positioning), they just focus on understanding glue and know that new products will happen almost accidentally (like post-it-notes.)
So this doesn't mean competitive positioning isn't important - you still need to find a differentiated or cost leadership position, it's just that this isn't where the company's energy goes. They focus on core competencies, and get competitive positioning thrown into the bargain.
The suggestion is that this is a more sustainable basis for competition. In the 1960s and 70s it may have ben possible to hang onto a competitive positioning but these days your competitors will jump in straight after you and your lovely clear blue water will quickly turn purple and then red. But it's harder for competitors to copy your core competencies so this type of competitive strategy is more sustainable.
By the way, people are also a small part of a core competency, but it is a small part which is often overlooked. But at least this is better than simply being part of a support activity as in Porter''s competitive positioning (and it's interesting to note that the point at which we started talking about core competencies was around the same time we started to get interested in HR being more strategic too.)
So, for the business, core competencies mean the business can compete more sustainably. And for HR it means we're a small enabler to this success, and no longer just a support function